1. Field of Invention
The present invention relates to an advanced process control (APC) system and an APC method. More particularly, the present invention relates to an APC system and an APC method utilizing virtual metrology (VM) with a reliance index (RI).
2. Description of Related Art
Run-to-run (R2R) advanced process control (APC) is widely applied to semiconductor and TFT-LCD factories for improving process capability. As defined in SEMI E133 specification, a R2R control is the technique of modifying recipe parameters or the selection of control parameters between runs to improve processing performance. A (process) run can be a batch, a lot, or an individual workpiece, wherein the R2R APC becomes a lot-to-lot (L2L) APC when a run is a lot, and the R2R APC becomes a workpiece-to-workpiece (W2W) APC when a run is a workpiece. A workpiece may represent a wafer for the semiconductor industry or a glass for the TFT-LCD industry. The L2L APC is now widely implemented for dealing with advanced technologies. When a L2L control is applied, only one single workpiece in the lot is required to be measured for feedback and feedforward control purposes. However, as the device dimension shrinks further, tighter process control is needed. In this case, the L2L control may not be accurate enough and therefore a W2W control becomes essential for critical stages. As a result, each workpiece in the lot should be measured. To fulfill this requirement, large amounts of metrology tools will be required and production cycle time will also be increased significantly. Furthermore, metrology delays, which are inevitable as real measurements are performed, will not only cause complicated control problems but also degrade the APC performance.
To resolve the problem mentioned above, virtual metrology (VM) was proposed. Virtual metrology is a technology using a conjecture model to predict metrology variables using information about the state of the process for every workpiece. If the VM conjecture model is fresh and accurate enough, it can generate a VM value within seconds after collecting the complete tool process data of a workpiece. Therefore, this VM value can be applied for real-time W2W control.
Referring to FIG. 1, FIG. 1 is a schematic block diagram showing a conventional model of EWMA (Exponentially Weighted Moving Average) R2R control disclosed by the paper entitled “Performance Analysis of EWMA Controllers Subject to Metrology Delay”, M.-F. Wu, C.-H. Lin, D. S.-H. Wong, S.-S. Jang, and S.-T. Tseng, published in IEEE Transactions on Semiconductor Manufacturing, vol. 21, no. 3, pp. 413-425, August 2008, which is incorporated herein by reference. Let us consider a process model with linear input and output relationship:yk=β0+β1uk+ηk  (1)where yk is the plant output; uk the control action taken for process run k; β0 the initial bias of process; β1 the process gain; and η5 the disturbance model input.
Given a process predictive model Auk, where A is a gain parameter (e.g., removal rate for chemical mechanical polishing (CMP)) estimated for the system, and its initial values can be obtained from the actual tool/recipe performance.
Using an EWMA (Exponentially Weighted Moving Average) filter, the model offset or disturbance of the (k+1)th process run is estimated to be{tilde over (η)}k+1=α(yk−Auk)+(1−α){tilde over (η)}k  (2)where α is an EWMA coefficient ranged between 0 and 1.
Control action of (k+1)th process run is
                              u                      k            +            1                          =                              Tgt            -                                          η                ~                                            k                +                1                                              A                                    (        3        )            where Tgt represents the target value.
Referring to FIG. 2, FIG. 2 is a schematic block diagram showing a conventional W2W control scheme utilizing virtual metrology (VM), wherein yz is the zth process run of actual measurement value of the sampling product (workpiece) measured by a metrology tool 20; ŷk is the kth process run of VM data; and Xk is the kth process run of process data of a process tool 10. In the paper entitled “On the Quality of Virtual Metrology Data for Use in the feedback Process Control”, A. A. Khan, J. R. Moyne, and D. M. Tilbury, published in Proc. AEC/APC Symposium XIX—North America, Palm Springs, Calif. USA, September 2007; the paper entitled “An Approach for Factory-Wide Control Utilizing Virtual Metrology”, A. A. Khan, J. R. Moyne, and D. M. Tilbury, published in IEEE Transactions on Semiconductor Manufacturing, vol. 20, no. 4, pp. 364-375, November 2007; and the paper entitled “Virtual Metrology and Feedback Control for Semiconductor Manufacturing Process Using Recursive Partial Least Squares”, A. A. Khan, J. R. Moyne, and D. M. Tilbury, published in Journal of Process Control, vol. 18, pp. 961-974, 2008, which are incorporated herein by reference, Khan et al. proposed a W2W control scheme utilizing VM. Khan et al. proposed to modify the above equation (2) for a R2R controller 40 as follows:
When yk is measured by the actual metrology tool 20, it becomes yz, an EWMA coefficient α, is used in{tilde over (η)}k+1=α1(yz−Auk)+(1−α1){tilde over (η)}k  (4)
When yk is conjectured or predicted by a VM module 30, it becomes ŷk, i.e. a VM value ŷk and an EWMA coefficient α2 is used in{tilde over (η)}k+1=α2(ŷk−Auk)+(1−α2){tilde over (η)}k  (5)
Khan et al. pointed out that α1>α2 (usually, depending on the relative quality of virtual metrology data). Now, the controller-gain problem of applying VM is focused on how to set α2, wherein the rule of thumb is that α2 should depend on the quality or reliability of VM and α2<α1. Khan et al. proposed two VM quality metrics to consider incorporating VM quality into the controller gain of a R2R controller 40:                1. Prediction error at metrology runs:Error=y−ŷ  (6)        2. If y and ŷ are zero-mean Gaussian deviations from targets, then Min mean-square-error (MSE) estimator of y based on ŷ is        
                              y          mmse                =                  ρ          ⁢                                    σ              y                                      σ                              y                ^                                                                        (        7        )            where the correlation coefficient
                    ρ        =                              cov            ⁡                          [                              y                ,                                  y                  ^                                            ]                                                          σ              y                        ⁢                          σ                              y                ^                                                                        (        8        )            and σy and σŷ are standard deviations of y and ŷ, respectively.
Nevertheless, both metrics proposed above have the following disadvantages:                1. Both equations (6) & (7) need actual metrology data “y”; however, if actual metrology data (measurement values) (y) are available, then no virtual metrology value (ŷ) are needed at all.        2. The value of ymmse may not be normalized to be between 0˜1 because ymmse may be positive or negative due top ρ.        
As a result, it may not be easy to combine the data quality metrics as in equations (6) and (7) into the R2R model. Hence, there is a need to develop an APC system and an APC method utilizing VM with a reliance index (RI) and a global similarity index (GSI) for effectively considering the data quality of VM into the R2R controller.